Brett A. Bednarcyk

An efficient implementation of the generalized method of cells for unidirectional, multi-phased composites with complex microstructures

An efficient implementation of the generalized method of cells micromechanics model is presented that allows analysis of periodic unidirectional composites characterized by repeated unit cells containing thousands of subcells. The original formulation, given in terms of Hills strain concentration matrices that relate average subcell strains to the macroscopic stains, is reformulated in terms of the interfacial subcell tractions as the basic unknowns. This is accomplished by expressing the displacement continuity equations in terms of the stresses and then imposing the traction continuity conditions directly. The result is a mixed formulation wherein the unknown interfacial subcell traction components are related to the macroscopic strain components. Because the stress field throughout the repeating unit cell is piece-wise uniform, the imposition of traction continuity conditions directly in the displacement continuity equations, expressed in terms of stresses, substantially reduces the number of unknown subcell traction (and stress) components, and thus the size of the system of equations that must be solved. Further reduction in the size of the system of continuity equations is obtained by separating the normal and shear traction equations in those instances where the individual subcells are, at most, orthotropic. Comparison of execution times obtained with the original and reformulated versions of the generalized method of cells demonstrates the new versions efficiency. As demonstrated through examples, the reformulated version facilitates previously unattainable detailed analysis of the impact of fiber cross-section geometry and arrangement on the response of multi-phased unidirectional composites.

Transverse tensile and creep modeling of continuously reinforced titanium composites with local debonding

Abstract A new, widely applicable model for local interfacial debonding in composite materials is presented. Unlike its direct predecessors, the new model allows debonding to progress via unloading of interfacial stresses even as global loading of the composite continues. The primary advantages of this new model are its accuracy, simplicity, and efficiency. In order to apply the new debonding model to simulate the behavior of composite materials, it was implemented within the generalized method of cells (GMC) micromechanics model for general periodic multi-phased materials. The time- and history-dependent (viscoplastic) transverse tensile and creep behavior of SiC/Ti composites, which are known to be subject to internal fiber–matrix debonding, was then simulated. Results indicate that GMCs ability to simulate the transverse behavior of titanium matrix composites has been significantly improved by the new debonding model. Further, the present study has highlighted the need for a more accurate time, temperature, and rate dependent constitutive representation of the titanium matrix behavior in order to enable predictions of the composite transverse response, without resorting to recalibration of the debonding model parameters.

Micromechanics-based deformation and failure prediction for longitudinally reinforced titanium composites

Abstract Two models to account for fiber breakage in longitudinally loaded composite materials have been incorporated into NASA Glenns Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) (Arnold SM, Bednarcyk BA, Wilt TE, Trowbridge D. MAC/GMC Users Guide: Version 3.0. NASA/TM- 1999-209070, 1999). The first is Curtins widely used effective fiber breakage model (Curtin WA. Ultimate strengths of fibre-reinforced ceramics and metals. Composites 1993;24(2):98–102; Curtin WA. Theory of mechanical properties of ceramic-matrix composites. J Am Ceram Soc 1991;74(11):2837–45). This model treats all fibers in the composite as one effective fiber whose properties degrade in accordance with the statistical strength distribution of the actual fibers. The second is a new discrete model that considers failure of many individual fibers in a composite repeating unit cell. This model explicitly includes the important feature of local stress unloading in fractured fibers, even as global loading of the composite continues. MAC/GMC was employed to simulate the longitudinal tensile deformation and failure behavior of several silicon-carbide-fiber/titanium-matrix (SiC/Ti) composites using both models. Through comparison with experiment, MAC/GMC, in conjunction with the incorporated fiber breakage models, is shown to be quite realistic and capable of accurate predictions for various temperatures, fiber volume fractions, and fiber diameters.

Micromechanics-Based Modeling of Woven Polymer Matrix Composites

A novel approach is combined with the generalized method of cells (GMC) to predict the elastic properties of plain-weave polymer matrix composites (PMCs). The traditional one-step three-dimensional homogenization procedure that has been used in conjunction with GMC for modeling woven composites in the past is inaccurate due to the lack of shear coupling inherent in the model. However, by performing a two-step homogenization procedure in which the woven composite repeating unit cell is homogenized independently in the through-the-thickness direction prior to homogenization in the plane of the weave, GMC can now accurately model woven PMCs. This two-step procedure is outlined and implemented, and predictions are compared with results from the traditional one-step approach as well as other model and experimental results from the literature. Full coupling of this two-step technique within the recently developed Micromechanics Analysis Code with GMC software package will result in a widely applicable, efficient, and accurate tool for the design and analysis of woven composite materials and structures.

Inelastic Response of a Woven Carbon/Copper Composite— Part II: Micromechanics Model

Part II of this paper presents a detailed development of an efficient micromechanics model for woven metal matrix composites (MMCs). The approach was to employ Aboudis (1995) three-dimensional generalized method of cells (GMC-3D) as a global model, and to embed Aboudis (1987) original method of cells within GMC-3D as a local model. Inelastic deformation is modeled on the local level, in the original method of cells. For this reason the field quantities must be passed between the local and global models continuously, as opposed to using the local model once simply to determine local effective properties. This process is computationally intensive, and GMC-3D, in its original form, is not adequately efficient to analyze refined composite geometries. Hence, GMC-3D was reformulated using mixed concentration equations rather than traditional strain concentration equations, improving the models computational efficiency considerably. The model is now capable of readily analyzing the thermomechanical behavior of elaborate and varied woven and braided composites. Experimental test results for a particular woven MMC, 8-harness satin carbon/copper, were presented in Part I of this paper. The predictions of the model described herein will be correlated with these experimental results in Part III.

Efficient Multiscale Modeling Framework for Triaxially Braided Composites using Generalized Method of Cells

In this paper, a framework for a three-scale analysis, beginning at the constituent response and propagating to the braid repeating unit cell (RUC) level, is presented. At each scale in the analysis, the response of the appropriate RUC is represented by homogenized effective properties determined from the generalized method of cells micromechanics theory. Two different macroscale RUC architectures are considered, one for eventual finite-element implementation and the other for material design, and their differences are compared. Model validation is presented through comparison to both experimental data and detailed finite-element simulations. Results show good correlation within range of experimental scatter and the finite-element simulation. Results are also presented for parametric studies varying both the overall fiber volume fraction and braid angle. These studies are compared to predictions from classical lamination theory for reference. Finally, the multiscale analysis framework is used to predict t...

Micromechanics Modeling of Composites Subjected to Multiaxial Progressive Damage in the Constituents

uniaxial stress–strain response. Local final-failure criteria are also proposed based on mode-specific strain energy release rates and total dissipated strain energy. The coupled micromechanics-damage model described herein is applied to a unidirectional E-glass/epoxy composite and a proprietary polymer matrix composite. Results illustrate thecapabilityofthecoupledmodeltocapturethevastlydifferentcharacterofthemonolithic(neat)resinmatrixand the composite in response to far-field tension, compression, and shear loading.

Micromechanics-based progressive failure analysis of composite laminates using different constituent failure theories

Predicting failure in a composite can be performed using ply level mechanisms and/or micro level mechanisms. This paper uses the generalized method of cells and high-fidelity generalized method of cells micromechanics theories, coupled with classical lamination theory, to study progressive damage in composites. Different failure theories, implemented at the fiber and matrix constituent level within a laminate, are investigated. A comparison is made among maximum stress, maximum strain, Tsai-Hill, and Tsai-Wu failure theories. To verify the failure theories, the Worldwide Failure Exercise experiments are used. The Worldwide Failure Exercise is a comprehensive study that covers a wide range of polymer matrix composite laminates. The objectives of this paper are to evaluate the current predictive capabilities of the generalized method of cells and high-fidelity generalized method of cells micromechanics theories for the progressive failure prediction of polymer matrix composite laminates and to evaluate the influence of four failure criteria applied at the fiber/matrix constituent scale. The numerical results demonstrate overall agreement with the experimental results for most of the composite layups examined, but also point to the need for more accurate resin damage progression models.

Analysis Tools for Adhesively Bonded Composite Joints, Part 2: Unified Analytical Theory

Adhesively bonded joints are currently of interest to the aerospace field due to the heavy reliance on bonded composite structures in new aircraft designs. In response, tools for joint analysis have been developed and examined in this two-part paper. In Part 1, a higher-order theory, considering an explicit discretization of the joint geometry, was investigated. In Part 2, a method for multiaxial stress analysis of composite joints is developed based on Mortensens unified approach, with considerable extension to accommodate transverse in-plane strain and hygrothermal loads and most importantly, to compute the in-plane and interlaminar stresses in the adherends. Compared with other analytical methods for bonded joint analysis, the present method is capable of handling more general situations, including various joint geometries, linear and nonlinear adhesives, asymmetric and unbalanced laminates, and various loading and boundary conditions. The method has been implemented within the commercially available HyperSizer® structural analysis software. Through comparison to finite element and analytical results, it is shown that the new HyperSizer joint analysis method is efficient and accurate and can serve as a capable tool for joint analysis in preliminary design, where rapid and generally accurate stress field estimates, as well as joint strengths and margins are needed.

Failure Analysis of Adhesively Bonded Composite Joints

Failure analysis of bonded composite joints is essential to the design of modern aerospace vehicles in which adhesive joints are widely used. Recently, methods for stress and failure analysis of composite bonded joints have been developed in a new HyperSizer® capability. The first part of the capability involves calculation of adhesive stresses, as well as detailed in-plane and out-of-plane stresses in the adherends, as described in ref. 1. This companion paper presents the second major part, which is the prediction of failure of bonded joints and validation of those predictions. Many leading bonded joint failure theories, summarized herein, were implemented, and then evaluated for accuracy against test data. Through comparison to 14 test cases with 3 different joint configurations, the ratios of predicted failure load divided by test average failure load vary from 0.77 to 0.95. These results show that HyperSizer is relatively accurate and consistent for predicting initial failure.